Abstract: Unramified Whittaker functions and their analogues occur naturally in number theory as terms in the Fourier expansions of automorphic forms. Precise information about these functions is useful in many aspects of study, such as in the construction of L-functions. In this paper, the method of Casselman and Shalika is used to derive explicit values for the analogue of the unramified Whittaker function in a distinguished model that arises in connection with quadratic base change.